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- Title
Exponential Diophantine equations for correlation functions of Tchebyscheff maps.
- Authors
ZHOU Xing-Wang
- Abstract
Tchebyscheff map is a typical chaotic map and the correlation functions play a key role in the study of its statistical properties. This paper aims at the solutions of a class of exponential Diophantine equations arising in the calculation of correlation functions of the Tchebyscheff map. To solve the equation, we firstly reduce it to a new Diophantine equation with strictly increasing exponentials and nonzero coefficients. Then we introduce the definition of "block" and classify the reduced equations based on the number of blocks constructing the equation, thus transform the problem of solving the equation to solve the new equations constructed by blocks. Finally we solve the equations constructed by one block and two blocks and exemplify the application of the main results.
- Subjects
DIOPHANTINE equations; STATISTICAL correlation; PROBLEM solving
- Publication
Journal Of Sichuan University (Natural Sciences Division) / Sichuan Daxue Xuebao-Ziran Kexueban, 2023, Vol 60, Issue 6, p1
- ISSN
0490-6756
- Publication type
Article
- DOI
10.19907/j.0490-6756.2023.061006